Whiting was the daughter of Joel Whiting, a teacher, and Elizabeth Comstock. In 1865 she graduated from Ingham University (the first university for women in the United States) at LeRoy, N.Y. She then taught classes at Ingham and later in Brooklyn, N.Y., where she began to attend scientific lectures.

In 1876 Whiting became professor of physics at Wellesley College in Massachusetts, a new institution of higher education for women that had opened the year before. To learn about the new method of laboratory physics in which students were required to use laboratory instruments to make measurements, she became a guest in the physics classes of Edward Pickering at the Massachusetts Institute of Technology. The physics laboratory that Whiting subsequently established at Wellesley in 1878 was the first for women and only the second in the United States.

In 1880 Whiting began teaching astronomy classes at Wellesley. One of her earliest—and most famous—students was the American astronomer Annie Jump Cannon. In 1895, inspired by newspaper accounts of German physicist Wilhelm Röntgen’s discovery of X-rays, Whiting made the first X-ray photographs in the United States. In 1900 the Whitin Observatory was built, of which Whiting was the first director. The observatory contained a 12-inch (30-cm) refracting telescope purchased from the Clark family of telescope makers, as well as a transit telescope and several spectroscopes. (Spectroscopy was a particular interest of hers.) In 1912 she retired from the physics department, and in 1916 she retired from the directorship of the Whitin Observatory.